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A debt can be paid off in three equal installments: $1000 now, $1000 in 3 years and...

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marrr | (Level 1) eNoter

Posted July 17, 2013 at 10:56 PM via web

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A debt can be paid off in three equal installments: $1000 now, $1000 in 3 years and $1000 in 6 years. What single payment can pay off the loan in  4 years form now, if interest is 10% per annum, compounded semi-anually?

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aruv | High School Teacher | (Level 2) Valedictorian

Posted July 18, 2013 at 2:04 AM (Answer #1)

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Let principle part in first and second installments are respectively x and y . Therefore

appy formula t calculate installments

`A=P(1+R/100)^n` , where A is amount ,P is principle,R% is rate per annum and n is number of conversion.

first installment will be

`1000=x(1.05)^6`

`746.22=x`

`and`

`1000=y(1.05)^12`

`556.84=y`

Thus total principle /debt=

1000+746.22+556.84=2303.06

Thus after four years ,it becomes

`A=2303.06(1.05)^8`

`=3402.67`

 

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